Show commands:
SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 102960.em
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.em1 | 102960i2 | \([0, 0, 0, -3507, -79934]\) | \(172531059372/9295\) | \(256988160\) | \([2]\) | \(98304\) | \(0.68069\) | |
102960.em2 | 102960i1 | \([0, 0, 0, -207, -1394]\) | \(-141915888/39325\) | \(-271814400\) | \([2]\) | \(49152\) | \(0.33412\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.em have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.em do not have complex multiplication.Modular form 102960.2.a.em
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.